Sure! I'll provide guidance for each of the questions you've listed.
Question 7: System Type
- System # 1: The classification would depend on whether matter and energy can enter or leave the system. Without specific details, I can't definitively classify it.
- System # 2: Similar to System # 1.
- System # 3: Same as above.
For context:
- Open system: Exchange of both energy and matter with surroundings.
- Closed system: Exchange of energy but not matter.
- Isolated system: No exchange of energy or matter.
Question 8: Mechanical Energy of Cake
The mechanical energy (E) of the cake consists of both its kinetic energy (KE) and potential energy (PE):
- Kinetic Energy (KE) = \( \frac{1}{2}mv^2 \)
- Potential Energy (PE) = \( mgh \)
Where:
- \( m = 4 , \text{kg} \)
- \( v = 5.0 , \text{m/s} \)
- \( h = 2.4 , \text{m} \)
- \( g = 9.81 , \text{m/s}^2 \)
Calculations:
-
\( KE = \frac{1}{2} \times 4 , \text{kg} \times (5.0 , \text{m/s})^2 \)
-
\( KE = 50 , \text{J} \)
-
\( PE = 4 , \text{kg} \times 9.81 , \text{m/s}^2 \times 2.4 , \text{m} \)
-
\( PE = 94.08 , \text{J} \)
Total Mechanical Energy: \[ E = KE + PE = 50 , \text{J} + 94.08, \text{J} = 144.08 , \text{J} \]
Question 9: Distance Travelled by Shark
Distance (d) can be calculated with: \[ d = speed \times time \]
Given:
- Speed = 6.0 m/s
- Time = 45.0 s
Calculation: \[ d = 6.0 , \text{m/s} \times 45.0 , \text{s} = 270 , \text{m} \]
Question 10: Non-solar Energy Source
One example of a non-solar energy source is geothermal energy. It is derived from the heat stored beneath the Earth's surface, which can be used for heating and electricity generation.
Question 11: Energy calculations
(a) Useful work (energy): 1500 J
(b) Energy input: 5000 J
(c) Energy output: To find this, we can assume it is equivalent to the useful work if no energy is lost except for waste. So it's 1500 J.
(d) The pot of water is a closed system since it exchanges energy (heating) but does not exchange matter with its environment.
(e) Wasted energy: \[ Wasted , Energy = Energy , Input - Useful , Work \] \[ = 5000 , \text{J} - 1500 , \text{J} = 3500 , \text{J} \]
(f) Percent efficiency: \[ Efficiency = \left(\frac{Useful , Energy}{Energy , Input}\right) \times 100% \] \[ = \left(\frac{1500 , \text{J}}{5000 , \text{J}}\right) \times 100% = 30% \]
Question 12: Pythagorean Theorem and Trigonometry Questions
These depend on a specific triangle. You would use:
- Pythagorean theorem \( a^2 + b^2 = c^2 \) to find the missing side.
- Trigonometric functions like sin, cos, and tan for angles.
Question 13: Scalar or Vector
(a) Weight: vector
(b) 150°C: scalar
(c) 56cm [W]: vector
(d) 12.54km: scalar
(e) 67m/s² [W]: vector
Question 14: Work Done
Work done \( W \) is calculated as: \[ W = Force \times Distance \] Given:
- Force = 25 N
- Distance = 40.0 m Calculation: \[ W = 25 , \text{N} \times 40.0 , \text{m} = 1000 , \text{J} \]
Unit for work is J (Joules).
Question 15: Mass of Penguin
Kinetic energy (KE) is given by: \[ KE = \frac{1}{2}mv^2 \] Given:
- KE = 30 J
- v = 2.5 m/s
Rearranging for mass (m): \[ m = \frac{2 \times KE}{v^2} = \frac{2 \times 30 , \text{J}}{(2.5 , \text{m/s})^2} \] \[ m \approx 9.6 , \text{kg} \]
Question 16: Matching Words
- Acceleration
- Speed
- Elastic potential energy
- Electrical
- Fission
Question 17: Work Input
Work done (W) is calculated by: \[ W = F \times d \] Given:
- F = 800 N
- d = 5.0 m Calculation: \[ W = 800 , \text{N} \times 5.0 , \text{m} = 4000 , \text{J} \]
If efficiency is 50%, input work is doubled to 8000 J: \[ \text{Work input} = \frac{4000 , \text{J}}{0.50} = 8000 , \text{J} \]
Question 18: Speed of Balloon
The kinetic energy (KE) when fired is equal to the potential energy (PE) at the maximum height: \[ PE = mgh \] \[ KE = \frac{1}{2}mv^2 \]
Setting them equal: \[ mgh = \frac{1}{2}mv^2 \] Solving for speed when height is 12.0 m.
Rearrange (m cancels out): \[ v = \sqrt{2gh} = \sqrt{2 \times 9.81 , \text{m/s}^2 \times 12.0 , \text{m}} \]
Calculate: \[ v ≈ 15.5 , \text{m/s} \]
Question 19: Kinetic and Gravitational Potential Energy
On Earth, gravitational potential energy depends on the height (h) and mass (m); it will be greater on Earth than Neptune due to the stronger gravitational acceleration. The kinetic energy (which is based on speed) would remain constant unless acted upon by forces. Therefore, while the gravitational potential energy of a box of cookies will be greater on Earth because of its higher gravity (approximately 9.81 m/s² compared to Neptune's 11.15 m/s²), the kinetic energy depends on how fast it’s moving.
Question 20: Parrot's Height
(a) The gravitational potential energy (PE) is given by \( PE = mgh \), so to find height: \[ h = \frac{PE}{mg} = \frac{65, \text{J}}{(1.4, \text{kg})(9.81, \text{m/s}^2)} \]
Calculating gives: \[ h ≈ 4.77 , \text{m} \]
(b) The type of potential energy in the fireplace is chemical potential energy, since it derives from the stored energy in the natural gas.
Feel free to ask for any specific calculations or clarifications!
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